A Thermal Lattice Boltzmann Two-Phase Flow Model and Its Application to Heat Transfer Problems—Part 1. Theoretical Foundation

[+] Author and Article Information
Peng Yuan

Mechanical Engineering Department, University of Pittsburgh, Pittsburgh, PA, 15261pey1@pitt.edu

Laura Schaefer

Mechanical Engineering Department, University of Pittsburgh, Pittsburgh, PA, 15261laschaef@engr.pitt.edu

J. Fluids Eng 128(1), 142-150 (Aug 10, 2005) (9 pages) doi:10.1115/1.2137343 History: Received December 18, 2004; Revised August 10, 2005

A new and generalized lattice Boltzmann model for simulating thermal two-phase flow is described. In this model, the single component multi-phase lattice Boltzmann model proposed by Shan and Chen is used to simulate the fluid dynamics. The temperature field is simulated using the passive-scalar approach, i.e., through modeling the density field of an extra component, which evolves according to the advection-diffusion equation. By coupling the fluid dynamics and temperature field through a suitably defined body force term, the thermal two-phase lattice Boltzmann model is obtained. In this paper, the theoretical foundations of the model and the validity of the thermal lattice Boltzmann equation method are laid out, illustrated by analytical and numerical examples. In a companion paper (P. Yuan and L. Schaefer, 2006, ASME J. Fluids Eng., 128, pp. 151–156), the numerical results of the new model are reported.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Discrete velocity vectors for some commonly used 2-D and 3-D particle speed models

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Figure 2

Streamlines of 2-D lid-driven cavity flow at Re=103

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Figure 3

Velocity profiles for u along the vertical geometric centerline of the cavity

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Figure 4

Maximum and minimum density values as a function of ∣gf∣

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Figure 5

Density ratio as a function of ∣gf∣

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Figure 6

Density contours plot in the xy plane at z=25 (symmetry plane)

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Figure 7

Velocity vectors plot in the xy plane at z=25 (symmetry plane)

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Figure 8

The maximum magnitude of spurious currents changes with ∣gf∣

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Figure 9

Density contours for different values of gw (different wettabilities): (a) gw=0.06, θ=120.6° and (b) gw=−0.03, θ=71.3°

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Figure 10

Velocity fields for different values of gw: (a) gw=0.06 and (b) gw=−0.03

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Figure 11

The relation between the contact angle θ of the bubble and the fluid/solid interaction strength gw

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Figure 12

Velocity vectors and isotherms at Ra=5000 and Pr=1.0: (a) velocity vectors and (b) isotherms

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Figure 13

Growth rate of instability vs Ra number

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Figure 14

Isotherms at steady state obtained by the LBE method

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Figure 15

Nusselt number at the top wall with respect to the time step obtained by the LBE method





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